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\begin{document}
\title{Electron phase separation involving superconductivity in the extended Hubbard models with pair hopping interaction}
\author{\underline{Konrad Kapcia}}
\affiliation{Electron States of Solids Division, Faculty of Physics, \mbox{Adam Mickiewicz University in Pozna\'n, Umultowska 85, 61-614 Pozna\'n, Poland}}
\author{Stanis\l{}aw Robaszkiewicz}
\affiliation{Electron States of Solids Division, Faculty of Physics, \mbox{Adam Mickiewicz University in Pozna\'n, Umultowska 85, 61-614 Pozna\'n, Poland}}
\begin{abstract}
In this work the extended Hubbard models with pair hopping interaction (at atomic limit) are investigated within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation (exact in $d\rightarrow+\infty$) [1-4].
The exact results derived  for $d=1$ and approximated results for various lattices at $d<+\infty$ are also presented [1,2,4].
We analyze mutual stability of  the superconducting (SS) phase and charge (CO) or magnetic (F) orderings as well as homogeneous mixed phases [3,4].
Our results show that the SS phase can coexist with the CO or F phases only in states with electron phase separation.


\textbf{References:}
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{\scriptsize[1] K. Kapcia, S. Robaszkiewicz, R. Micnas, J. Phys.: Condens. Matter \textbf{24},  235601 (2012)}

{\scriptsize[2] K. Kapcia, S. Robaszkiewicz,  J. Phys.: Condens. Matter \textbf{25},  065603 (2013)}

{\scriptsize[3] K. Kapcia, J. Supercond. Nov. Magn. \textbf{26},  2647 (2013); Acta Phys. Pol. A \textbf{121},  733 (2012)}

{\scriptsize[4] K. Kapcia, PhD Thesis, Adam Mickiewicz University (2014)}
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\textit{The work has been financed by NCN as a project No. DEC-2011/01/N/ST3/00413 and as the doctoral scholarship No. DEC-2013/08/T/ST3/00012 as well as by ESF--OP Human Capital--POKL.04.01.01-00-133/09-00.}
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